Cosmological behavior of a hyperbolic solution in f(Q) gravity

Abstract

In this work, we study the universe’s dynamics in the context of f(Q) gravity by use of a flat FLRW model. Two particular forms are considered: $f\left(Q\right)=Q-\lambda Q$ and $f\left(Q\right)=Q-\lambda Q^2$, where Q and $\lambda$ represent the nonmetricity and arbitrary constant, respectively. We take a special form for the scale factor, $a=sinh{\left(t\right)}^{\frac{1}{\alpha }}$, to solve the Friedmann field equations within the f(Q) formalism. The scale factor’s behavior is here determined by the model parameter $\alpha$. In our model, we primarily analyze the behavior of the equation of state parameter $\omega$. We examine the scalar field and examine the resultant solution’s energy conditions. We use a number of diagnostic techniques, including the Jerk, Om, and statefinder diagnostic tools, to validate our model. We also include the observational constraints from the BAO and Hubble databases. A thorough explanation of the outcomes and the model is given.